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Toggle Joint.

constant. D is the virtual centre, and D p, D w the radii; and the
triangle p E B being similar, p B may represent P's constant
velocity, while P E shews that of W. The latter being transferred
to B p, gives points in the curve shewn; reaches infinity in the
direction B/, and nothing in the direction B/r W is then respec-
tively in the positions w and wr

The Toggle Joint has many useful applications, the stone-
breaker and wagon-brake (Fig. 463") being examples. In Fig. 462
the joint is seen to consist of a simple slider-crank chain, o is
the virtual centre, and OP, o w the radii. Producing w p to c,

vel. P      B p

vel. W


and several points, such as F, will form the polar curve B F D,
showing W's velocity, where P's velocity is uniform and repre-
sented by B P. The curve is a semicircle, having A as centre.

Cooke's Mine Ventilator in Fig. 464 is a case of the
quadric chain. Crank and shutter shafts are connected by link
CD, and AB is a fixed though virtual link. Two positions are
shown, the shaded air being drawn in, while the dotted air is
pushed out by the rotation of the drum.

Quick-Return Motion.—See Fig. 457.

Valve Motion for engines needs examination only for
point paths, and will be treated in Chapter X.

Parallel Motions should strictly be termed straight-line
motions^ but are now best known by the first title. Watt's
(Fig. 465) is the simplest. A D and B c being equal, the upward
movement of p will be vertically straight, because D curves to the
left by the same amount as c deviates to the right. This is
extremely near the truth when a is below 20°, but not absolutely
so. Thus :—


-j  (I -COS a)

sin /3 = sin a + — (i - cos 0)

Deviation of P from )         r
vertical                    ~

f              ^^ n\

/   = ~ (COS a - COS /3)

assuming c D to be vertical at central position.